Bring a small pot of water to a boil, carefully lower the egg in, and cook for 6.5 minutes before transferring to an ice bath.
In a medium saucepan, heat the toasted sesame oil over medium heat and sauté the sliced cremini mushrooms until they release their moisture and turn golden brown.
Stir in the minced garlic and grated fresh ginger, cooking for 1 minute until the aroma is fragrant.
Pour in the chicken bone broth and tamari, bringing the liquid to a gentle simmer.
Season the chicken breast with sea salt and black pepper, then add it to the simmering broth along with the soba noodles.
Simmer for 6-8 minutes until the chicken is opaque and the noodles are tender, then remove the chicken and shred it with two forks.
Return the shredded chicken to the pot and stir in the fresh spinach until it wilts into the broth.
Peel the cooled egg and slice it in half.
Pour the soup into a large bowl, top with the egg halves and sliced green onion, and serve immediately.